Mathematics

Problem

Let

x

be the length of one of the equal sides of an isosceles triangle, and let

\theta

be the angle between them. If

x

is increasing at the rate

\left(\frac{1}{12}\right)

m/hr, and

\theta

is increasing at the rate of

\frac{\pi}{180}

radians/hr then the rate in

\text{m}^2/\text{hr}

at which the area of the triangle is increasing when

x = 12

m and

\theta = \frac{\pi}{4}

: (A)

2^{1/2}\left(1 + \frac{2\pi}{5}\right)

(B)

\frac{73}{2} \cdot 2^{1/2}

(C)

\frac{3^{1/2}}{2} + \frac{\pi}{5}

(D)

2^{1/2}\left(\frac{1}{2} + \frac{\pi}{5}\right)